A new correlation coefficient for bivariate time-series data

• We introduce a new correlation coefficient taking the lag difference of data points.
• We investigate the properties of this new correlation coefficient.
• New correlation coefficient captures the cross-independence of two variables over time.
• New coefficient is compared with the Pearson and DCCA coefficients via simulations.

The correlation in time series has received considerable attention in the literature. Its use has attained an important role in the social sciences and finance. For example, pair trading in finance is concerned with the correlation between stock prices, returns, etc. In general, Pearson’s correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use. Here, we introduce a new correlation coefficient which takes into account the lag difference of data points. We investigate the properties of this new correlation coefficient. We demonstrate that it is more appropriate for showing the direction of the covariation of the two variables over time. We also compare the performance of the new correlation coefficient with Pearson’s correlation coefficient and Detrended Cross-Correlation Analysis (DCCA) via simulated examples.